Foundations of Engineering Acoustics


  • Frank Fahy, Institute of Sound and Vibration Research, University of Southampton, UK
  • Frank Fahy, Institute of Sound and Vibration Research, University of Southampton, UK

Foundations of Engineering Acoustics takes the reader on a journey from a qualitative introduction to the physical nature of sound, explained in terms of common experience, to mathematical models and analytical results which underlie the techniques applied by the engineering industry to improve the acoustic performance of their products. The book is distinguished by extensive descriptions and explanations of audio-frequency acoustic phenomena and their relevance to engineering, supported by a wealth of diagrams, and by a guide for teachers of tried and tested class demonstrations and laboratory-based experiments.Foundations of Engineering Acoustics is a textbook suitable for both senior undergraduate and postgraduate courses in mechanical, aerospace, marine, and possibly electrical and civil engineering schools at universities. It will be a valuable reference for academic teachers and researchers and will also assist Industrial Acoustic Group staff and Consultants.
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Undergraduate, postgraduate, engineers in acoustics


Book information

  • Published: September 2000
  • ISBN: 978-0-12-247665-5


“...a masterpiece of thoroughness, organization, and clarity...sure to become a classic in acoustical literature and should be on the shelves of every acoustics library.” — Jorge P. Arenas, Auburn University, International Journal of Acoustics and Vibration, Vol. 6, No. 1, 2001 “essentially a text book aimed at senior undergraduate, and post graduate engineering students, and their tutors ... However, the scope and format are also suitable for professional engineers with no formal training in acoustics...Foundations of Engineering Acoustics does great service to the field of acoustics by providing an appropriate introduction to the practical implications of noise and vibration in engineering and everyday life in general.” — Donald Quinn, Institute of Acoustics Bulletin “...there are very few textbooks that present Engineering Acoustics at a fairly basic, though higher than elementary, level. Professor Fahy's book therefore meets a need on the part of many engineers who may lack a formal background in acoustics but nonetheless are faced with acquiring some knowledge of the subject...Questions are occasionally interposed in the text, and these should help to stimulate the thought processes of the reader. The occasional flashes of humor are welcome...One feels that Professor Fahy has succeeded in his purpose," assist readers to acquire an understanding of those concepts and principles, physical phenomena, theoretical models and mathematical representations that form the foundations of the practice of engineering acoustics"...the reader who carefully reads and works his way through this text will acquire a very good understanding of the physics involved in a wide range of engineering acoustics and vibration applications, as well as the mathematical basis for tackling more advanced problems...Overall, Frank Fahy has written a book that is up to the standard of erudition, authoritativeness and pedagogical excellence that we have come to expect from him on the basis of his other publications.” — Applied Acoustics, Vol. 66, Issue 1, January 2005 “I found that this book serves its purpose as a comprehensive introduction to acoustics for the upper level engineering student. I can also recommend the text as a refresher for the practicing engineer.” — Stephen M. Jaeger, Colin Gordon & Associates, San Bruno, CA, USA

Table of Contents

PrefaceAcknowledgmentsChapter 1 Sound Engineering 1.1 The Importance of Sound 1.2 Acoustics and the Engineer 1.3 Sound the ServantChapter 2 The Nature of Sound and Some Sound Wave Phenomena 2.1 Introduction 2.2 What Is Sound? 2.3 Sound and Vibration 2.4 Sound in Solids 2.5 a Qualitative Introduction to Wave Phenomena 2.5.1 Wavefronts 2.5.2 Interference 2.5.3 Reflection 2.5.4 Scattering 2.5.5 Diffraction 2.5.6 Refraction 2.5.7 The Doppler Effect 2.5.8 Convection 2.6 Some More Common Examples of the Behavior of Sound WavesChapter 3 Sound in Fluids 3.1 Introduction 3.2 The Physical Characteristics of Fluids 3.3 Molecules and Particles 3.4 Fluid Pressure 3.5 Fluid Temperature 3.6 Pressure, Density and Temperature in Sound Waves in a Gas 3.7 Particle Motion 3.8 Sound in Liquids 3.9 Mathematical Models of Sound Waves 3.9.1 The Plane Sound Wave Equation 3.9.2 Solutions of the Plane Wave Equation 3.9.3 Harmonic Plane Waves: Sound Pressure 3.9.4 Plane Waves: Particle Velocity 3.9.5 The Wave Equation in Three Dimensions 3.9.6 Plane Waves in Three Dimensions 3.9.7 The Wave Equation in Spherical Coordinates 3.9.8 The Spherically Symmetric Sound Field 3.9.9 Particle Velocity in the Spherically Symmetric Sound Field 3.9.10 Other Forms of Sound FieldChapter 4 Impedance 4.1 Introduction 4.2 Some Simple Examples of the Utility of Impedance 4.3 Mechanical Impedance 4.3.1 Impedance of Lumped Structural Elements 4.4 Forms of Acoustic Impedance 4.4.1 Impedances of Lumped Acoustic Elements 4.4.2 Specific Acoustic Impedance of Fluid in a Tube at Low Frequency 4.4.3 Normal Specific Acoustic Impedance 4.4.4 Radiation Impedance 4.4.5 Acoustic Impedance 4.4.6 Line and Surface Wave Impedance 4.4.7 Modal Radiation Impedance 4.5 an Application of Radiation Impedance of a Uniformly Pulsating Sphere 4.6 Radiation EfficiencyChapter 5 Sound Energy and Intensity 5.1 The Practical Importance of Sound Energy 5.2 Sound Energy 5.3 Transport of Sound Energy: Sound Intensity 5.4 Sound Intensity in Plane Wave Fields 5.5 Intensity and Mean Square Pressure 5.6 Examples of Ideal Sound Intensity Fields 5.6.1 The Point Monopole 5.6.2 The Compact Dipole 5.6.3 Interfering Monopoles 5.6.4 Intensity Distributions in Orthogonally Directed Harmonic Plane Wave Fields 5.7 Sound Intensity Measurement 5.8 Determination of Source Sound Power Using Sound Intensity Measurement 5.9 Other Applications of Sound Intensity MeasurementChapter 6 Sources of Sound 6.1 Introduction 6.2 Qualitative Categorization of Sources 6.2.1 Category 1 Sources 6.2.2 Category 2 Sources 6.2.3 Category 3 Sources 6.3 The Inhomogeneous Wave Equation 6.3.1 Sound Radiation by Foreign Bodies 6.3.2 Boundary 'Sources' Can Reflect or Absorb Energy 6.4 Ideal Elementary Source Models 6.4.1 The Dirac Delta Function 6.4.2 The Point Monopole and the Pulsating Sphere 6.4.3 Acoustic Reciprocity 6.4.4 External Forces on a Fluid and the Compact Dipole 6.4.5 The Oscillating Sphere 6.4.6 Boundary Sources 6.4.7 Free-Field and Other Green's Functions 6.4.8 The Rayleigh Integrals 6.5 Sound Radiation from Vibrating Plane Surfaces 6.6 The Vibrating Circular Piston and the Cone Loudspeaker 6.7 Directivity and Sound Power of Distributed Sources 6.7.1 Sound Power of a Source in the Presence of a Second Source 6.8 Zones of a Sound Field Radiated by a Spatially Extended Source 6.9 Experimental Methods for Source Sound Power Determination 6.10 Source CharacterizationChapter 7 Sound Absorption and Sound Absorbers 7.1 Introduction 7.2 The Effects of Viscosity, Thermal Diffusion and Relaxation Processes on Sound in Gases 7.2.1 The Origin of Gas Viscosity 7.2.2 The Effects of Thermal Diffusion 7.2.3 The Effect of Molecular Relaxation 7.2.4 Sound Energy Dissipation at the Rigid Boundary of a Gas 7.2.5 Acoustically Induced Boundary Layers in a Gas-Filled Tube 7.3 Forms of Porous Sound Absorbent Material 7.4 Macroscopic Physical Properties of Porous Sound-Absorbing Materials 7.4.1 Porosity 7.4.2 Flow Resistance and Resistivity 7.4.3 Structure Factor 7.5 The Modified Equation for Plane Wave Sound Propagation in Gases Contained within Rigid Porous Materials 7.5.1 Equation of Mass Conservation 7.5.2 Momentum Equation 7.5.3 The Modified Plane Wave Equation 7.5.4 Harmonic Solution of the Modified Plane Wave Equation 7.6 Sound Absorption by a Plane Surface of Uniform Impedance 7.6.1 The Local Reaction Model 7.6.2 Sound Power Absorption Coefficient of a Locally Reactive Surface 7.6.3 Wave Impedance 7.7 Sound Absorption by Thin Porous Sheets 7.7.1 The Immobile Sheet in Free Field 7.7.2 The Limp Sheet in Free Field 7.7.3 The Effect of a Rigid Wall Parallel to a Thin Sheet 7.8 Sound Absorption by Thick Sheets of Rigid Porous Material 7.8.1 The Infinitely Thick 'Sheet' 7.8.2 The Sheet of Finite Thickness 7.8.3 The Effect of a Backing Cavity on the Sound Absorption of a Sheet of Porous Material 7.9 Sound Absorption by Flexible Cellular and Fibrous Materials 7.10 The Effect of Perforated Cover Sheets on Sound Absorption by Porous Materials 7.11 Non-Porous Sound Absorbers 7.11.1 Helmholtz Resonators 7.11.2 Panel Absorbers 7.12 Methods of Measurement of Boundary Impedance and Absorption Coefficient 7.12.1 The Impedance Tube 7.12.2 Reverberation Room MethodChapter 8 Sound in Waveguides 8.1 Introduction 8.2 Plane Wave Pulses in a Uniform Tube 8.3 Plane Wave Modes and Natural Frequencies of Fluid in Uniform Waveguides 8.3.1 Conservative Terminations 8.3.2 Non-Conservative Terminations 8.4 Response to Harmonic Excitation 8.4.1 Impedance Model 8.4.2 Harmonic Response in Terms of Green'S Functions 8.5 a Simple Case of Structure-Fluid Interaction 8.6 Plane Waves in Ducts that Incorporate Impedance Discontinuities 8.6.1 Insertion Loss and Transmission Loss 8.6.2 Transmission of Plane Waves through an Abrupt Change of Crosssectional Area and an Expansion Chamber 8.6.3 Series Networks of Acoustic Transmission Lines 8.6.4 Side Branch Connections to Uniform Acoustic Waveguides 8.6.5 The Side Branch Tube 8.6.6 The Side Branch Orifice 8.6.7 The Helmholtz Resonator Side Branch 8.6.8 Bends in Otherwise Straight Uniform Waveguides 8.7 Transverse Modes of Uniform Acoustic Waveguides 8.7.1 The Uniform Two-Dimensional Waveguide with Rigid Walls 8.7.2 The Uniform Two-Dimensional Waveguide with Finite Impedance Boundaries 8.7.3 The Uniform Waveguide of Rectangular Cross-Section with Rigid Walls 8.7.4 The Uniform Waveguide of Circular Cross-Section with Rigid Walls 8.8 Harmonic Excitation of Waveguide Modes 8.9 Energy Flux in a Waveguide of Rectangular Cross-Section with Rigid Walls 8.10 Examples of the Sound Attenuation Characteristics of Lined Ducts and Splitter Attenuators 8.11 Acoustic Horns 8.11.1 Applications 8.11.2 The Horn EquationChapter 9 Sound in Enclosures 9.1 Introduction 9.2 Some General Features of Sound Fields in Enclosures 9.3 Apology for the Rectangular Enclosure 9.4 The Impulse Response of Fluid in a Reverberant Rectangular Enclosure 9.5 Acoustic Natural Frequencies and Modes of Fluid in a Rigid-Walled Rectangular Enclosure 9.6 Modal Energy 9.7 The Effects of Finite Wall Impedance on Modal Energy-Time Dependence in Free Vibration 9.8 The Response of Fluid in a Rectangular Enclosure to Harmonic Excitation by a Point Monopole Source 9.9 The Sound Power of a Point Monopole in a Reverberant Enclosure 9.10 Sound Radiation into an Enclosure by the Vibration of a Boundary 9.11 Probabilistic Wave Field Models for Enclosed Sound Fields at High Frequency 9.11.1 The Modal Overlap Factor and Response Uncertainty 9.11.2 High-Frequency Sound Field Statistics 9.11.3 The Diffuse Field Model 9.12 Applications of The Diffuse Field Model 9.12.1 Steady State Diffuse Field Energy, Intensity and Enclosure Absorption 9.12.2 Reverberation Time 9.12.3 Steady State Source Sound Power and Reverberant Field Energy 9.13 a Brief Introduction to Geometric (Ray) AcousticsChapter 10 Structure-Borne Sound 10.1 The Nature and Practical Importance of Structure-Borne Sound 10.2 Emphasis and Content of the Chapter 10.3 The Energy Approach to Modeling Structure-Borne Sound 10.4 Quasi-Longitudinal Waves in Uniform Rods and Plates 10.5 The Bending Wave in Uniform Homogeneous Beams 10.5.1 A Review of the Roles of Direct and Shear Stresses 10.5.2 Shear Force and Bending Moment 10.5.3 The Beam Bending Wave Equation 10.5.4 Harmonic Solutions of the Bending Wave Equation 10.6 The Bending Wave in Thin Uniform Homogeneous Plates 10.7 Transverse Plane Waves in Flat Plates 10.8 Dispersion Curves, Wavenumber Vector Diagrams and Modal Density 10.9 Structure-Borne Wave Energy and Energy Flux 10.9.1 Quasi-Longitudinal Waves 10.9.2 Bending Waves in Beams 10.9.3 Bending Waves in Plates 10.10 Mechanical Impedances of Infinite, Uniform Rods, Beams and Plates 10.10.1 Impedance of Quasi-Longitudinal Waves in Rods 10.10.2 Impedances of Beams in Bending 10.10.3 Impedances of Thin, Uniform, Flat Plates in Bending 10.10.4 Impedance and Modal Density 10.11 Wave Energy Transmission through Junctions Between Structural Components 10.12 Impedance, Mobility and Vibration Isolation 10.13 Structure-Borne Sound Generated by Impact 10.14 Sound Radiation by Vibrating Flat Plates 10.14.1 The Critical Frequency and Radiation Cancellation 10.14.2 Analysis of Modal Radiation 10.14.3 Physical Interpretations and Practical ImplicationsChapter 11 Transmission of Sound through Partitions 11.1 Practical Aspects of Sound Transmission through Partitions 11.2 Transmission of Normally Incident Plane Waves through an Unbounded Partition 11.3 Transmission of Sound through an Unbounded Flexible Partition 11.4 Transmission of Diffuse Sound through a Bounded Partition in a Baffle 11.5 Double-Leaf Partitions 11.6 Transmission of Normally Incident Plane Waves through an Unbounded Double-Leaf Partition 11.7 The Effect of Cavity Absorption 11.8 Transmission of Obliquely Incident Plane Waves through an Unbounded Double-Leaf Partition 11.9 Close-Fitting Enclosures 11.10 A Simple Model of a Noise Control Enclosure 11.11 Measurement of Sound Reduction Index (Transmission Loss)Chapter 12 Reflection, Scattering, Diffraction and Refraction 12.1 Introduction 12.2 Scattering by a Discrete Body 12.3 Scattering by Crowds of Rigid Bodies 12.4 Resonant Scattering 12.4.1 Discrete Scatterers 12.4.2 Diffusors 12.5 Diffraction 12.5.1 Diffraction by Plane Screens 12.5.2 Diffraction by Apertures in Partitions 12.6 Reflection by Thin, Plane Rigid Sheets 12.7 Refraction 12.7.1 Refracted Ray Path through a Uniform, Weak Sound Speed Gradient 12.7.2 Refraction of Sound in the AtmosphereAppendix 1 Complex Exponential Representation of Harmonic Functions A1.1 Harmonic Functions of Time A1.2 Harmonic Functions of Space A1.3 CER of Traveling Harmonic Plane Waves A1.4 Operations on Harmonically Varying Quantities Represented by CERAppendix 2 Frequency Analysis A2.1 Introduction A2.2 Categories of Signal A2.3 Fourier Analysis of Signals A2.3.1 The Fourier Integral Transform A2.3.2 Fourier Series Analysis A2.3.3 Practical Fourier Analysis A2.3.4 Frequency Analysis by Filters A2.4 Presentation of the Results of Frequency Analysis A2.5 Frequency Response Functions A2.6 Impulse ResponseAppendix 3 Spatial Fourier Analysis of Space-Dependent Variables A3.1 Wavenumber Transform A3.2 Wave DispersionAppendix 4 Coherence and Cross-Correlation A4.1 Background A4.2 Correlation A4.3 Coherence A4.4 The Relation between the Cross-Correlation and Coherence FunctionsAppendix 5 The Simple Oscillator A5.1 Free Vibration of the Undamped Mass-Spring Oscillator A5.2 Impulse Response of the Undamped Oscillator A5.3 The Viscously Damped Oscillator A5.4 Impulse Response of the Viscously Damped Oscillator A5.5 Response of a Viscously Damped Oscillator to Harmonic ExcitationAppendix 6 Measures of Sound, Frequency Weighting and Noise Rating Indicators A6.1 Introduction A6.2 Pressure-Time History A6.3 Mean Square Pressure A6.4 Sound Pressure Level A6.5 Sound Intensity Level A6.6 Sound Power Level A6.7 Standard Reference CurvesAppendix 7 Demonstrations and Experiments A7.1 Introduction A7.2 Demonstrations A7.2.1 Noise Sources A7.2.2 Sound Intensity and Surface Acoustic Impedance A7.2.3 Room Acoustics A7.2.4 Miscellaneous A7.3 Formal Laboratory Class Experiments A7.3.1 Construct a Calibrated Volume Velocity Source (CVVS) A7.3.2 Source Sound Power Determination Using Intensity Scans, Reverberation Time Measurements and Power Balance A7.3.3 Investigation of Small Room Acoustic Response A7.3.4 Determination of Complex Wavenumbers of Porous Materials A7.3.5 Measurement of the Specific Acoustic Impedance of a Sheet of Porous Material A7.3.6 Measurement of the Impedance of Side Branch and in-Line Reactive Attenuators A7.3.7 Sound Pressure Generation by a Monopole in Free Space and in a Tube A7.3.8 Mode Dispersion in a Duct A7.3.9 Scattering by a Rough Surface A7.3.10 Radiation by a Vibrating PlateAnswersBibliographyReferencesIndex